Journal of Mathematical Chemistry

, Volume 2, Issue 3, pp 267–277

How to compute the Wiener index of a graph

  • Bojan Mohar
  • Tomaž Pisanski
Notes

DOI: 10.1007/BF01167206

Cite this article as:
Mohar, B. & Pisanski, T. J Math Chem (1988) 2: 267. doi:10.1007/BF01167206

Abstract

The Wiener index of a graphG is equal to the sum of distances between all pairs of vertices ofG. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to compute the distances in a graph, and these can easily be adapted for the calculation of the Wiener index. An algorithm that calculates the Wiener index of a tree in linear time is given. It improves an algorithm of Canfield, Robinson and Rouvray. The question remains: is there an algorithm for general graphs that would calculate the Wiener index without calculating the distance matrix? Another algorithm that calculates this index for an arbitrary graph is given.

Copyright information

© J.C. Baltzer AO, Scientific Publishing Company 1988

Authors and Affiliations

  • Bojan Mohar
    • 1
    • 2
  • Tomaž Pisanski
    • 1
    • 2
  1. 1.Department of Ma theima ticsUniversity E.K. of LjubljanaLjubljanaYugoslavia
  2. 2.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada